No, it's not identity theft. The state is not pretending to be you to commit some kind of fraud or other crime. Rather, what you fear is that the business receiving the garnishment order might somehow misuse it after it gets the order or might be careless in safeguarding your information which would allow someone to commit identity theft. If that were to happen you'd have a remedy against that business. But until then you've not suffered any harm from this and thus have nothing for which to sue. You cannot successfully sue for what might happen in the future.
You don't need that. What you do is consult a lawyer who practices in the area of privacy law (or whatever area of law you need help with). That's one of the things lawyers are there for.

